Given the required predicates:
eats(x,y) : x eats y
food(x) : x is food
killed(x) : x is killed
I am confused as to how to represent this statement in First Order Logic
Would it be
$\forall(xy)eats(x,y)\wedge \neg killed(x)\to food(y)$
Or
$\forall(xy)eats(x,y)\wedge food(y) \to \neg killed(x)$
Or is it something else all together. An explanation along with the answer would be greatly appreciated.
I would read the statement as "For all $x$: If ($x$ has an eater $y$) and ($y$ is not killed), then ($x$ is food)"
$\exists y\ eats(y, x)$: There is some $y$ that eats $x$
$\neg killed(y)$: $y$ was not killed
$food(x)$: $x$ is food
$$\forall x(\exists y\ eats(y, x)\wedge\neg killed(y)\implies food(x))$$